Update
I now have a cognitive endurance goal of 15 poms total a day. Of these, I expect to use around ~5 for mathematics, and the remainder for programming and maybe a bit of Go language study. The calculations for math are a bit weird, but I expect them to balance out overall: treat 45 XP of MA as equivalent to two poms, and the 90 minutes of math study — split into two session of 45 minutes each, one per stream, as described below — as 3 poms. This slightly under-counts the time spent here — by ~10 minutes, if we assume 1min/XP — which I’m willing to let go, in return for being able to have a more leisurely experience of the whole thing, say by being able to brew and drink tea etc during the poms.
I have also added a third ‘stream’ to my mathematics study. This brings the number of ‘streams’ to a total of three: MA for the skeleton of a subject plus a fluency in doing it, along with studying what I need to know for other things; a second stream for building up mathematics at the deep hyperobject immersion level from scratch (or at least, from the relative basics); and a third more exploratory stream that meanders in obedience to the inscrutable exhortations of my soul. (This one isn’t part of the hyperobject-construction-and-deep-understanding-and-playing track; that’s purely for the second stream.) I suspect that this last stream will mostly be me satisfying my curiosity about various topics that I may not necessarily want to ‘study’, given the weight and intensity of what that word now implies for me.
Right now, I’m exploring number theory, using Kuldeep Singh’s book. (MA has already introduced some primitive concepts here as part of the MoP curriclulum.)
EDIT: OK, decided against this; after doing the (heh) math, this is one of the things that doesn’t fit in the time I have for mathematics right now, alas.
- Endurance: 7/12 poms
- Mathematics:
- MathAcademy: 45 XP; 77% MoP.
- Jacobs: 193/640 pages.
- First time I applauded the genius of the proof of the theorem that two lines making the same angle with a transversal are parallel. Neat! Yeah, OK, it’s not like the most complicated thing, sure, whatever, but like, beautiful! So simple, yet so cool. Jacobs (2nd edition) is a marvel of presentation.
- Though I’d recommend using the beginning of 3rd edition (up to the ‘We cannot go on like this’(?) point) so that the need for the rigorous presentation, and what it brings, are clear, are clearly felt.
- This also gives me an appreciation of the central/centrally load-bearing role of inequalities in classical geometry.
- First time I applauded the genius of the proof of the theorem that two lines making the same angle with a transversal are parallel. Neat! Yeah, OK, it’s not like the most complicated thing, sure, whatever, but like, beautiful! So simple, yet so cool. Jacobs (2nd edition) is a marvel of presentation.
Reflection
I notice that the way I’m thinking when I do geometry is now based on mental operations that don’t really exist in the ‘proofs’ as written down. Things like deformations, taking a point on a line segment and pulling it in a direction and seeing the resultant triangle, moving a line around an intersection as a pivot point to check whether some relation holds, etc; none of these are formally covered, but they’re what I’m actually doing when I ‘do’ geometry, or solve problems, or whatever? Interesting. Wonder how many others have bothered to document this ’esoteric’ part of the thought process. This is a thing which seems like it’d be central in teaching, yet is seldom ever even mentioned, much less formally taught?
And I have a suspicion that many things are like this. Eg, after learning Clojure, I find that the way I think about programming is in terms of data transformations of sequences (or mappings, I guess), perhaps with some consideration of access patterns, rather than indexical manipulations of storage arrays. It seems like what I was doing before anyway, but Clojure just made it clearer? (And kinda mandatory, given the immutability of everything.)
Also, the number theory books should really give geometric intuition and meaning for what the Euclidean algorithm does, geometrically: using ruler and compass to show the smaller being cut out of the larger, and this process continuing until one finds finally an amount that’s a measure of the two, how this is independent of absolute lengths, and why this corresponds to the GCD when considered numerically (since that’s what the GCD is), and how to run the algorithm is ‘reverse’ (so to speak) to find out how to ‘unfold’ the constructed geometric measure back recursively to a sum/difference of the original lengths, including how that comes about. This was quite important for my understanding, and I’m not sure why it isn’t either more common, or even the default method.